Analysis for polymer mixtures in solution utilizing electrophoretic light scattering apparatus

ABSTRACT

An electrophoretic scattering apparatus for determining the electrophoretic mobility and diffusion coefficient of a macromolecular polymer in solution is disclosed. More particularly, the charged macromolecules are driven through the solution by an electric field developed between two charged electrodes in a modified electrophoretic cell. The electric field is alternately enabled and disabled during the determination to prevent excessive heat build-up in the solution and the resultant convection of macromolecules which would distort the measurements. A laser provides an incident light beam which is passed through the cell perpendicular to the direction of the macromolecule flow so that the autocorrelation function or, alternatively, the frequency spectrum of the light scattered from the macromolecules can be observed at low scattering angles. The scattered light, in addition to having a frequency distribution curve proportional to the diffusion coefficient of the macromolecules, is Doppler shifted by an amount proportional to the electrophoretic mobility of the macromolecule in the scattering region. Because each species of polymers has a unique electrophoretic mobility and hence Doppler shift, the apparatus is useful in quantitatively analyzing a mixture of several different polymers in solution (e.g., life-like enzymes such as blood) to identify the polymers and their relative concentrations.

ANALYSIS FOR POLYMER MIXTURES IN SOLUTION UTILIZING ELECTROPHORETICLIGHT SCATTERING APPARATUS Inventors: Willis ll. Flygare, Urbana, 111.;

Bennie R. Ware, Arlington, Mass.

[73] University of Illinois Foundation,

Urbana, 111.

Filed: Aug. 2, 1973 Appl. No.: 385,055

Related U.S. Application Data Division of Ser. No. 309,272, Nov. 24,1972, Pat. No. 3,766,048.

Assignee:

U.S. Cl. 204/180 R, 204/299 Int. Cl B0lk 5/00 Field of Search 204/180 R,299

References Cited UNITED STATES PATENTS 12/1971 Dilworth 204/299 l/l973Bean 204/299 10/1973 Greenwood et al. 204/299 2/1974 Flower et al204/299 Primary Examiner-T. Jung Assistant Examiner-A. C. PrescottAttorney, Agent, or Firm-Merriam, Marshall, Shapiro & Klose Mar. 11,1975 [57] ABSTRACT An electrophoretic scattering apparatus fordetermining the electrophoretic mobility and diffusion coefficient of amacromolecular polymer in solution is disclosed. More particularly, thecharged macromolecules are driven through the solution by an electricfield developed between two charged electrodes in a modifiedelectrophoretic cell. The electric field is alternately enabled anddisabled during the determination to prevent excessive heat build-up inthe solution and the resultant convection of macromolecules which woulddistort the measurements. A laser provides an incident light beam whichis passed through the cell perpendicular to the direction of themacromolecule flow so that the autocorrelation function or,alternatively, the frequency spectrum of the light scattered from themacromolecules can be observed at low scattering angles. The scatteredlight, in addition to having a frequency distribution curve proportionalto the diffusion coefficient of the macromolecules, is Doppler shiftedby an amount proportional to the electrophoretic mobility of themacromolecule in the scattering region. Because each species of polymershas a unique electrophoretic mobility and hence Doppler shift, theapparatus is useful in quantitatively analyzing a mixture of severaldifferent polymers in solution (e.g., life-like enzymes such as blood)to identify the polymers and their relative concentrations.

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ANALYSIS FOR POLYMER MIXTURES IN SOLUTION UTILIZING ELECTROPHORETICLIGHT SCATTERING APPARATUS This is a division of application Ser. No.309,272, filed Nov. 24, 1972, now U.S. Pat. No, 3,766,048.

BACKGROUND OF THE INVENTION The present invention relates generally toan apparatus for determining the electrical characteristics of polymersin solution and more particularly to an apparatus combiningelectrophoresis techniques with laser beat frequency spectroscopy forquantitatively analyzing mixtures of polymers in solution.

Heretofore, a standard laboratory technique commonly knows aselectrophoresis has been used to experimentally determine certainelectrical characteristics of polymers, e.g., their electrophoreticmobility and diffusion coefficient. Having determined thesecharacteristics for various polymers, electrophoresis techniques havebeen used to quantitatively analyze polymer mixtures, identifying thedifferent species of polymers in the mixture and their relativeconcentrations. K

One typical prior art arrangement utilizes a Tiselius electrophoresiscell wherein macromolecular polymers are initially restricted to aportion of the cell by a boundary. An electrophoresis cell of this typealso includes electrodes for generating an electric field across thecell perpendicular to the boundary so that the charged macromoleculesare attracted to the electrode of opposite polarity located on the otherside of the boundary. Accordingly, when the boundary is removed, eachmacromolecule moves through a gel or other supportive medium toward thatelectrode at a velocity determined by its own particular electrophoreticmobility, the consistency of the gel] and the strength of the electricfield. Different species of polymers having differing electrophoreticmobilities, depending on factors such as their size, shape and charge,however, so that they move with different velocities responsive to theelectric field.

Consequently, the component polymers comprising a mixture can beidentified by determining their respective electrophoretic mobilitieswhich are proportional to their displacement from the boundary at apredetermined time after removal of the boundary. Further, the width ofthe resultant distribution curve for any particular species of polymersis representative of that polymers diffusion coefficient, thereby aidingin its identification. Finally, the total area under the distributioncurve is indicative of the relative concentrations of the variouspolymers in the mixture. Thus, once the electrical characteristics of aparticular polymer have been determined, that polymer can subsequentlybe identified in a mixture of polymers in solution throughelectrophoresis. v

One disadvantage of prior art electrophoresis, however, is that it doesnot provide a value for the electrophoretic mobilities of themacromolecules in a solution. That is, because the results differdepending on the gel or other supporting medium used, there is alwayssome doubt raised as to whether the supporting medium is degrading thesample or otherwise introducing other factors into the analysis.

Another primary disadvantage is that the charged macromolecules may besubjected to convection due to the test results.

SUMMARY OF THE lNVENTlON The electrophoretic light scattering apparatusof the present invention employs the frequency analysis of scatteredlight to determine the electrophoretic mobility and diffusioncoefficient of a macromolecular polymer in solution. Further, theapparatus may be utilized to quantitatively analyze a mixture ofpolymers in solution (e.g., life-like enzymes such as blood) to identifythe polymers and their relative concentrations. The apparatus includesan electrophoretic cell containing the solution to be investigated.Means are included for applying an electric field across the solution ofcharged macromolecules, causing them to move at a constant velocity in adirection parallel to the electric field. The electric field isalternately enabled and disabled so that higher electric fields may beused without generating excessive heat build-up in the solution withattendant convection of the macromolecules. A source of monochromaticeletromagnetic radiation provides an incident light beam intersectingthe path of the charged macromolecules in the scattering region of theelectrophoretic cell so that the radiation scattered from the chargedmacromolecules is Doppler shifted due to their translational motion.Because different species of polymers move through the solution withdifferent velocities, depending on their respective electrophoreticmobilities, a particular amount of Doppler shift is characteristic of asingle species of polymers. Accordingly, detector means are alsoincluded for analyzing the Doppler shift and frequency distribution ofthe scattered light to determine the electrophoretic mobilities anddiffusion coefficients of the various polymers and to identify thedifferent polymers and their relative concentrations in the solution.

BRIEF DESCRIPTION OF THE DRAWINGS The features of this invention whichare believed to be novel are set forth with particularity in theappended claims. The invention together with its further objects andadvantages thereof, may be'best understood, however, by reference to thefollowing description taken in conjunction with the accompanyingdrawings, in which like reference numerals identify like elements in theseveral figures and in which:

FIG. 1 is a block diagram of electrophoretic light scattering apparatusin accordance with a preferred embodiment of the invention;

FIGS. 2a and 2b are representative of the autocorrelation function andcorresponding power spectrum, respectively, of a mixture ofmacromolecular polymers in solution;

FIG. 3 is a perspective view of an electrophoretic cell which may beutilized in conjunction with the electrophoretic light scatteringapparatus of the present invention; and

FIG. 4 is a top elevational view of the electrophoretic cell shown inFIG. 3.

PREFERRED EMBODIMENT OF THE INVENTION Referring now to FIG. 1, asolution of macromolecular polymers (e.g., blood) that has been dialyzedto a known pH and ionic strength is filtered into a modifiedelectrophoretic cell through millipore filters which remove anyexcessively large particles.

The electrophoretic cell 10 includes a pair of electrodes 11 fordeveloping an electric field therebetween whenever a pulse generator 12applies a potential to the electrodes 11. Application of the electricfield to the solution causes the charged macromolecules to migrate in adirection parallel to the electric field toward the electrode ofopposite polarity. The drift velocity (V,,) of each individualmacromolecule, in turn, is equal to its electrophoretic mobility (a)times the electric field strength (E). Thus, the different species ofpolymers move through the solution at different velocities responsive toa constant electric field, depending on various factors, such as theirsize, shape and charge, which combine to determine their correspondingelectrophoretic mobility. It should be understood, of course, thatvariations in the net charge of the macromolecules can be effected bychanging the pH and/or the ionic strength of the solution. Accordingly,the electrophoretic mobilities can be modified to move themacromolecules through the solution at a slower rate to increase theresolution between different species of macromolecular polymers.

As previously mentioned, the strength of the electric field that can beapplied across the solution when prior art electrophoresis techniquesare utilized is limited to levels where the charged macromolecules willnot be subject to convection due to resistive heating of the solution.The electrophoretic light scattering apparatus of the present invention,however, facilitates the quantitative analysis ofa mixture of polymersin solution so that an experiment may be completed in less than 1 hour.Moreover, the potential applied to the electrodes 11 by generator 12 ispulsed so that higher fields that are typically used in electrophoresiscan be employed. That is, because the interval between pulses isnormally five to ten times the pulse duration, there is ample time forany heat generated by the passage of the current through the solution tobe dissipated. The pulses are also of alternating polarity to preventthe formation of concentration gradients.

A laser 13 provides a source of monochromatic electromagnetic radiationthat is applied to a region in the solution between the electrodes 11designated to be the scattering region. Although the selection of aparticular laser and the angle of incidence of the light beam is solelya design consideration, in the present embodiment the incident light issupplied by an Ar laser 13 on the 5145 Angstrom line and applied to thescattering region in a direction normal to the electric field foroptimum results. During intervals when the electric field is pulsed on,causing the charged macromolecules to migrate toward the electrode ofopposite polarity, the incident light beam is scattered and Doppershifted by each macromolecule as it moves with a constant drift velocityparallel to the electric field through the scattering region. Themagnitude of the Dopper shift is directly proportional to the velocityand, as a result, the electrophoretic mobility of the macromolecule.Consequently, for mixtures of polymers, each particular species producesa Dopper shift of the incident light representative of its owncorresponding electrophoretic m0- bility. Thus, the electric fieldshifts the spectral frequency distributions of a mixture of differentpolymers having distinct electrophoretic mobilities to differentfrequency centers.

The diffusion, or random motion. of the charged macromoleculescomprising a particular species of polymers also gives rise to thecreation and decay of concentration fluctuations. creating a Lorentzianfrequency distribution of scattered light with half-width proportionalto the diffusion coefficient of that particular polymer. Although eachpolymer in a species has the same electrophoretic mobility, thediffusion of the macromolecules in directions other than parallel to theelectric field broadens the frequency spectrum of the light scattered bymacromolecules of the species.

The spectrum of Doppler shifted light scattered from the solution at aparticular scattering angle 0 is collimated over a predetermineddistance to a photomultiplier 14 (e.g., RCA No. 7265) where it isdetected and subsequently mixed, or heterodyned, with a component of theincident light beam to permit analysis of the lower difference, or beat,frequencies by audio frequency apparatus. This technique is morecommonly known as heterodyne beat frequency spectroscopy.

It is evident from FIG. 1 that the distance between scatteringmacromolecules which is probed in the solution depends on the scatteringangle 0. When Bis small (forward scattering), large spatial differencesin the solution are probed. When 6 is large (back scattering). on theother hand, distances are probed which approach the wavelength of theincident radiation. It is clear that the concentration fluctuations in asolution of macromolecules will decay or be created at a slower rate forlarger distances in the solution. Thus, low angle scattering leads tonarrower-width frequency distributions than high angle scattering.Further, at low scattering angles, the incident light substantiallyexceeds the intensity of the scattered light, so that heterodyning canbe accomplished.

The resulting signal can be analyzed by measuring either itsautocorrelation function, C(r), which is a measure of the correlationbetween concentration fluctuations in a solution of macromolecules or,alternatively, by measuring its frequency spectrum. In any event,according to the Wicner-Khintchine theorem, the autocorrelationfunction, C(r), is related to the spectrum,

.I(w), of the scattered light by the equation:

mo flcma dr In the present embodiment, the detector includes anautocorrelator l7 (e.g., Fabri-Tek Model SD-75) which is associated withan averager 18 comprising a digital computer (e.g., Fabri-Tek Model1070). It should be understood, however, that the autocorrelator l7 canbe replaced by a specturm analyzer (not shown) to obtain the frequencyspectrum directly without Fourier transformation. To simplify thepresent description, however, it will be assumed that an autocorrelatoris being utilized. A trigger signal for pulse generator l2 is coupled tothe averager l8 simultaneously with the initiation of the electric fieldacross the electrophoretic cell 10. The detector is then delayed for apreselected time interval in order to allow the macromolecules in thesolution to reach a steady state at which time it determines theautocorrelation function for the polymer mixture. The electric field issubsequently removed until the system again reaches an equilibrium sothat a new measurement may be made.

The detector calculates the autocorrelation function ofthe photocurrentby holding the first data point, mul-' tiplying it by each successivedata point, and storing the products so that the autocorrelationfunction is repeatedly calculated and signal averaged. Finally, the datafrom averager I8 is taken out on paper tape for analysis. It the averagecorrelation function was determined, it may then be Fourier transformedto obtain the fre' quency spectrum. Thus, a typical electrophoreticlight scattering experiment in accordance with the present invention iscompleted in five minutes to one-hour as compared with the 12 to 48hours required for an electrophoresis experiment using prior artmethods.

An illustration of the autocorrelation function for a mixture ofpolymers in solution is shown in FIG. 2a, and the resulting spectrumderived therefrom by Fourier transformation is shown in FIG. 2b. Thevarious peaks identified generally at P in FIG. 2b corresponds todifferent polymers in the solution, their displacement (Af) from theorigin being representative of their electrophoretic mobilities. Also,the width of the peaks (P) is indicative of their different diffusioncoefficients while their amplitudes correspond to their relativeconcentrations in the solution. Thus, having previously determined thevarious electrical characteristics of known polymers, it is possible toquantitatively analyze an unknown solution containing a mixture ofpolymers.

The modified electrophoretic cell 10 shown in FIG. 3 is useful inperforming the electrophoretic light scattering experiments. Moreparticularly, the cell 10 includes a pair of Ag-AgCl electrodes 11inserted directly into the solution which, in turn, is contained in asubstantially U-shaped chamber. A narrow rectangular chamber connectsthe L-shaped tubes 22 comprising the sides" of U-shaped chamber.Accordingly, when a potential is applied to the electrodes 11, anelectric field running parallel with the length of chamber 20 isdeveloped. A light pipe 21 is provided to conduct the incident lightbeam to the portion of chamber 20 known as the scattering region so thatit is normal to the electrical field and hence the translational motionof the charged macromolecules in the solution. foolant is introducedinto a reservoir 23 encompassing most of the U-shaped chamber throughtube 24 so that a coolant circulated therein is in thermal contact withthe solution in the U-shaped chamber. The coolant, in turn, exitsthrough tube 25. A top view of the electrophoretic cell It) is shown inFIG. 4.

Accordingly, there has ben shown an apparatus for analyzing a mixture ofmacromolecular polymers, such as blood, by combining electrophoresistechniques with laser beat frequency spectroscopy to measure thefrequency distribution and the Doppler shift of light scattered from thepolymers in a solution under the influence of a pulsed electric field.The apparatus may be used to simultaneously measure the diffusioncoefficient and the electrophoretic mobility of the various chargedmacromolecules thereby providing a method of quantitatively analyzingmixtures of polymers in solution. In this manner, it is possible toidentify and determine the'relative concentrations ofthe variouspolymers comprising the mixture. Further, because the measurements areaccomplished in a relatively short period of time, the electric fieldapplied across the electrophoretic cell may be pulsed thereby reducingthe heat generated due to the current flowing between the electrodes.Also, by alternating the polarity of the pulses applied to theelectrodes, the electric field is reversed after each measurement sothat concentration gradients of the macromolecules are not formed duringthe experiment.

While a particular embodiment of the present invention has been shownand described, it will be obvious to those skilled in the art thatvarious changes and modifications may be made without departing from theinvention in its broader aspects. Accordingly, the aim in the appendedclaims is to cover all such changes and modifications as may fall withinthe true spirit and scope of the invention.

We claim;

1. A method of determining the electrophoretic mobility and diffusioncoefficient of a macromolecular polymer in solution, which methodcomprises the following steps:

establishing an electric field across said solution to move saidmacromolecules through said solution in a direction parallel with saidelectric field at a velocity proportional to said electrophoreticmobility;

applying a light beam comprising monochromatic electromagnetic radiationincident on said macromolecules;

detecting said light beam scattered by said macromolecules; heterodyningsaid detected scattered light beam with said incident light beam toproduce beat frequency signals; and

analyzing said beat frequency signals to determine the Doppler shift ofsaid scattered light beam which is reprsentative of said electrophoreticmobility and to determine the frequency distribution of said scatteredlight beam which is representative of said diffusion coefficient.

2. The method of claim 1 including alternately enabling and disablingsaid electric field during the determination of said electrophoreticmobility and said diffusion coefficient to reduce heat build-up in thesolution.

3. The method of claim 2 including delaying said analyzing for apredetermined time interval after said electric field is enabled toallow said macromolecules to reach a steady state.

4. The method of claim 1 wherein said analyzing comprisesautocorrelating and averaging said beat frequency signal.

1. A METHOD OF DETERMINING THE ELECTROPHORETIC MOBILITY AND DIFFUSIONCOEFFICIENT OF A MACROMOLECULAR POLYMER IN SOLUTION, WHICH METHODCOMPRISES THE FOLLOWING STEPS: ESTABLISHING AN ELECTRIC FIELD ACROSSSAID SOLUTION TO MOVE SAID MACROMOLECULES THROUGH SAID SOLUTION IN ADIRECTION PARALLEL WITH SAID ELECTRIC FIELD AT A VELOCITY PROPORTIONALTO SAID ELECTROPHORETIC MOBILITY; APPLYING A LIGHT BEAM COMPRISINGMONOCHROMATIC ELECTROMAGNETIC RADIATION INCIDENT ON SAID MACROMOLECULES;DETECTING SAID LIGHT BEAM SCATTERED BY SAID MACROMOLECULES; HETERODYNINGSAID DETECTED SCATTERED LIGHT BEAM WITH SAID INCIDENT LIGHT BEAM TOPRODUCE BEAT FREQUENCY SIGNALS; AND ANALYZING SAID BEAT FREQUENCYSIGNALS TO DETERMINE THE DOPPLER SHIFT OF SAID SCATTERED LIGHT BEAMWHICH IS REPRESENTATIVE OF SAID ELECTROPHORETIC MOBILITY AND TODETERMINE THE FREQUENCY DISTRIBUTION OF SAID SCATTERED LIGHT BEAM WHICHIS REPRESENTATIVE OF SAID DIFFUSION COEFFICIENT.
 1. A method ofdetermining the electrophoretic mobility and diffusion coefficient of amacromolecular polymer in solution, which method comprises the followingsteps: establishing an electric field across said solution to move saidmacromolecules through said solution in a direction parallel with saidelectric field at a velocity proportional to said electrophoreticmobility; applying a light beam comprising monochromatic electromagneticradiation incident on said macromolecules; detecting said light beamscattered by said macromolecules; heterodyning said detected scatteredlight beam with said incident light beam to produce beat frequencysignals; and analyzing said beat frequency signals to determine theDoppler shift of said scattered light beam which is reprsentative ofsaid electrophoretic mobility and to determine the frequencydistribution of said scattered light beam which is representative ofsaid diffusion coefficient.
 2. The method of claim 1 includingalternately enabling and disabling said electric field during thedetermination of said electrophoretic mobility and said diffusioncoefficient to reduce heat build-up in the solution.
 3. The method ofclaim 2 including delaying said analyzing for a predetermined timeinterval after said electric field is enabled to allow saidmacromolecules to reach a steady state.